Anarcho-capitalism and minarchism are two distinct strains of libertarianism.[1][2][3][4] Although anarcho-capitalists and minarchists agree on most political issues, they are sometimes hostile towards each other, particularly because most adherents of both philosophies support the non-aggression principle (NAP) and see the opposing philosophy as misrepresenting its political implications. Minarchists believe that it is the responsibility of the state to enforce NAP, while anarcho-capitalists see the state as a violation of NAP, and believe that all valuable services – including law and defense – are best provided in the marketplace.

Minarchists generally justify the state on the grounds that it is the logical consequence of adhering to the non-aggression principle. Some minarchists argue that anarchism is immoral because it implies that the non-aggression principle is optional. They argue that this is because the creation and enforcement of laws under anarchism is open to competition.[8] Others argue that competing defense or dispute resolution organizations lack a "court of final appeals" or "single arbitration network."[9][10] Another common justification is that private defense and court firms would tend to represent the interests of those who pay them enough.[11] Anarcho-capitalists generally argue that the state violates the non-aggression principle by its nature because governments use force against those who have not stolen private property, vandalized private property, assaulted anyone, or committed fraud.[12][13] Many also argue that monopolies tend to be corrupt and inefficient.

Anarcho-capitalists generally argue that private defense and court agencies would have to have a good reputation in order to stay in business. Furthermore, Linda & Morris Tannehill argue that no coercive monopoly of force can arise on a truly free market and that a government's citizenry can’t desert them in favor of a competent protection and defense agency.[14]

Libertarian philosopher Moshe Kroy argues that the disagreement between anarcho-capitalists who adhere to Murray Rothbard's view of human consciousness and the nature of values and minarchists who adhere to Ayn Rand's view of human consciousness and the nature of values over whether or not the state is moral is not due to a disagreement over the correct interpretation of a mutually held ethical stance. He argues that the disagreement between these two groups is instead the result of their disagreement over the nature of human consciousness and that each group is making the correct interpretation of their differing premises. These two groups are therefore not making any errors with respect to deducing the correct interpretation of any ethical stance because they do not hold the same ethical stance.[15]

The U.S. Libertarian Party sought to be a "big tent" party when it was founded by welcoming both factions into its midst. The 1974 Libertarian National Convention adopted the Dallas Accord, which made the platform of the Libertarian Party purposefully ambiguous on the desirability of the state's existence. This involved using such phrases as "where governments exist, they must not violate the rights of any individual" in the statement of principles. In 2006, delegates to a national convention added the following language to the section on "Crime and Justice": "Government exists to protect the rights of every individual including life, liberty and property." This led some to conclude that anarchists were no longer welcome in the party.[19][20]